It's quite certain, that Schopenhauer didn't understand this chapter at all, since he calls the a priori pure concepts of understanding here “contentless”, i.e. empty, eventhough the main reason Kant is here discussing is quite the contrary: what specifically constitutes the content of these pure concepts of understanding? To be sure, they are empty from actual objects, but this chapter is about the object a priori, i.e. according to possibility. What's here at stake, is the a priori structure of the possibility of actual objects, as the object a priori, of which the former must precede the latter.
So, what is the content of a priori pure concepts of understanding, which serves as the basis for the preceding possibility, according to which an actual object can a posteriori, be given in experience? Let's make some preliminary notions first. The word 'category', according to it's etymological meaning, means 'towards-which'. Kant's meaning for the word is precisely the same and he doesn't here differ from the first one to use this greek word in it's philosophical context, i.e. Aristotle. 'Undestanding' in Kant's sense is the ability to think with concepts and in it's a priori mode, pure understanding thinks “with” categories, or rather is categorical. Understanding is simply towards-which, and categories are it's structures quite like letters A and B are the elements of the syllable AB.
Towards-which does not have merely “empty” nothing as the what-content of it's about-which, as Schopenhauer thought, but the question here is centered on the what-content of the a priori categories, i.e. an internal object without a dogmatically assumed external object. This what-content is that which gives categories their unity as the about-which they are as it's belongings, quite like the accidents of a substance. An empty nothing could not give them unity, quite like mere empty nothing can't make syllable AB from letters A and B. It's the form of the syllable as the belonging-together of letters, which make out it's unifying shape. On the other hand, AB could in it's relation to the letters be considered their unifying matter, and Kant means it this way: the about-which is the matter of formal categories a priori.
What matters for Kant is, that this content should, as it's a part of a priori philosophy of the internal sense, be given purely internally. For Kant, the philosopher of a priori is not without any object at all. He has the a priori possible form of object, which serves as the a priori possible matter of object. Only together they work as the a priori possibility for the a posteriori actuality of empirical objects. This possibility of an empirical object is indeed a formal one, but as divided to formally-formal and materially-formal.
What then is the formal matter of formal form? It is time. A peak in the history of theology and philosophy preceding Kant gives helpful hints at understanding this, even though they're not completely necessary either here. The problems Kant faced through the history of theology and philosophy, or rather the questionable tradition of intertwining both, serves to expose his quite superficial motives for his conception of formal matter as time, since it's not good enough to understand that someone is wrong, but it should also be made an attempt to explain, why he was wrong. Otherwise the reason for being wrong would be merely accidental and not necessary. Great thinkers like Kant should not be suspected of making an accidental mistake, especially when the question is of extreme importance.
Kant is here related mainly to three thinkers, two of them theological and one philosophical, all of them huge impact both theologically and philosophically. The two theologians are Luther and Erasmus and the one philosopher is Descartes. Even though Erasmus is not by himself an important theologian, it is his confrontation with Luther which gives him a place in the history of great thinkers. From Luther Kant wanted to save the notion, that natural cognition can't reach any knowledge of God. On the other hand, Kant sided with Erasmus on the question about God's moral commands as revealed through man even without biblical, i.e. historical knowledge, shuch as the person of Christ. Kant tried to give some assent to both sides: to Luther from the side of theoretical use of reason, i.e. pure understanding as the region of nature, and to Erasmus from the side of practical use of reason, i.e. pure reason as the region of moral religion. It should be noted though, that Luther included such moral God in the natural use of reason as the wrath of the hidden un-christian God, “Deus absconditus“. Descartes stood in the way of Kant's theological synthesis, with his ultimately platonic theoretical proof about God. From Kan't ultimately theological perspective, Descartes had to be defeated on philosophical grounds before he could accomplish his great theological synthesis.
The main thrust of Descartes' philosophy, against which Kant had determined to invent a solution, even the quite artifical one he finally ended up with, concerns the question about the nature of time. In his famous philosophical theoretical proof of God, Descartes had tried to prove with absolute certainty, that theoretical cognition can't give itself it's own continuity in time. Accordingly theoretical cognition should depend on another principle, which provides that continuity in time. For Descartes, that another principle is God, which provides the theoretical subject's way out of itself, since otherwise it would not have temporal continuity. Descartes's God is here the platonic substance understood theoretically.
Kant is probably one of the few people who actually has understood Descartes's proof of God, even though Kant was, in the traditional sense of the word dogmatically against it, because of his ulterior theological motives. This is why Kant out of necessity came up with a different conception of time, which would make the theoretical subject self-sufficient in a way opposed to Descartes. This way there would be no need for a theoretical knowledge of the platonic substance and Luther's view of natural reason's impossibility to know God could be saved. On the other hand, Kant also couldn't accept Luther's view about belief in the historical figure of Christ as God, so he was compelled to make a point for the moral God of Erasmus.
These previous historical considerations give us evidence of the superficial motives in the background of Kant's conception of time as the formal matter of the categories of understanding. We'll now unfold Kant's “solution” and it's problem more precisely. First of all, why is the schema of a concept of understanding 'count' (Zahl)? 'Zahl' is not only 'number', but 'count', as if in “taking count”, i.e. “Zahl nehmen”, which means going through the manifold and numbering each one on the way. This numbering is counting and the result , or product of this counting is the count. So, Kant says, that the count by counting considers the counted manifold together as the unity of manifold. This manifold is not first encountered as such counted manifold, but counting must go through this act of counting to work as the unity of the counted manifold.
The counting itself, which goes through the manifold, and in a way produces it as the counted for the count, as such is first needed to make it a manifold. Count is a pure schema of a concept of the understanding, only when the counting has gone through and as such produced the manifold to be held schematically as the count of the manifold. The successive addition “from one to one (same of a kind)”, is the formal matter, on which the schema gives unity as a single representation. As the about-which of schema, this succession serves as the matter for the formal concept of understanding. This matter Kant calls a figure, or a picture (Bild). It is necessary for me here only to consider the category of quantity, although succession provides the towards-which also for the other categories, e.g. quality, relation and modality.
As an example of the picture, number 3 is quite an abstract concept, which can only be applied to a sensual image, such as 'xxx', but can't as such be made it's sensual image 'xxx', since it could also be presented by other figures, e.g. 'zzz'. What is not as evident is, that since the image is not the same as the concept, there must be something third in addition to the concept and picture, which gives their various relationships unity. This third member is the schema, which works in all images of abstract concepts of pure understanding. Schema gives the picture 'xxx' it's of-what, i.e. as the matter of number 3.
So time is the picture of the schema of number and as such works as the matter of the concept of pure understanding, which is a form. Time is the material-form, concept of count the formal-form, and transcendental schema the unifying transcendental judgement between both. In this particular transcendental judgement, the 'count' considered as a whole, is the concept of pure understanding applying through transcendental a priori judgement, or transcendental schema, to it's pictorial presentation, i.e. internal time. It's very noteworthy, that time is here interpreted as the matter of the internal sense, and as such purely a priori. This keeps time in the region of mere thinking, like Descartes' “res cogitans”, where it for Kant gives itself it's own continuity, instead of anything outside the thinking subject.
This way Kant tried to avoid the problem of Descartes's proof for God. A different solution to the question of time as merely an internal sense's matter, would also change the way Kant's conception of a priori can be considered acceptable. This doesn't mean that Descartes's solution to the problem of temporal dependence outside of the thinking subject could be considered right, i.e. platonic substance in it's theoretical sense. It must still be explained more clearly, why this question indeed is the crux deciding Kant's philosophy.
As the towards-which of all categories, internal succession of time, as counting, e.g. 1...2...3… and not 3, which would here be only the schema for formal quantity. This successive one-after-another as internal sense as a transcendental schema is more accurately based on the subject's a priori multiplicity and unity. The counting provides the matter for the form of subject in it's unity as understanding, where the matter is the subject's image as time. Time as the successive addition of one-after-another is not counting mathematical numbers, which I use only as an example, since such counting is according to Kant based on the subject's differing through it's time. Being the “of the same kind” in this succesion, subject becomes an image for itself, of which it's schema is this multiplicity brought in to union in the mere subject, i.e. a kind of would-be pure understanding without towards-which. Such understanding without towards-which as the what-content would not be pure understanding.
Without towards-which provided as the matter by internal succession of time, pure understanding would have no concept, since it would be a “predicate“ without it's content as about-what, and so it would not be a concept of pure understanding, i.e. a category. This would contradict the very concept Kant has for 'predicate'. As such, it would be “the first subject”, of which “nothing can be made” and which is for us a mere “nothing”, since it would be “only logical”, i.e. without any object corresponding it. Kant even uses here the word 'predicate' in stead of 'category', as 'praedicamentum' was the latin translation for the greek word 'katēgoria'. This “nothing” would be a mere 'dicamentum', without the 'prae-', i.e. before-what it is said and as such merely an empty term, and not a concept in Kant's meaning for a predicate, which is in line with the original meaning of Aristotle. Rather, this would be a mere self as pure reason, even though as pure reason it would not differ in it's possibility and actuality, as it necessarily does in critical philosophy.
For Kant this “object” in it's merely inner sense, is consciousness, which is collected in it's succession as pictorial time to a schematic unity, towards-which the self as pure understanding is. As such, the successive manifold of successive internal consciousnesses is brought before pure understanding's “first self”, constituting the categorical understanding as self-consciousness, having consciousness as it's form's content is predicative and thus not “nothing”. Hegel is quite right in calling Kant's substrate a self-consciousness, but this would be right only for Kant's philosophy and not his system of philosophy. This question has implications for the whole of Kant's philosophy of system, since it's the principle of the so called synthetic a priori judgements.
Kant's book Critique of pure reason, of which I've dealt only with one chapter, concerns only one part of Kant's philosophy as the critique of pure reason, i.e. the theoretical use of pure reason, which as practical would be quite different. Nevertheless, this one questions is decisive for the whole system even in reason's practical use, since it's theoretical use as understanding considers the possibility of the practical use of reason from the viewpoint of understanding. If, or rather since, the schema of possibility, which is also based on the subjectivity of “res cogitans”, is flawed in Kant's philosophy, also the actuality of this possibility as practical reason must be flawed. This whould also lead to another kind of interpretation of a priori, e.g. as a part of the history of being.
The schema of possibility is the agreement of the unity of different representations with the conditions of time, e.g. opposites can't exist at the same time in the same thing, but only after another. Since this is the philosophical possibility for the transition from the theoretical use of reason as a priori philosophy to pure practical use of reason as it's actuality, Kant's 'Noumenon' as the end of this transition in the total system, is conditioned through it's concept of possibility as impossible. This is contrary to Kant's belief, since it's necessary to exclude the intelligible world of 'Noumenon' even as a possibility, leaving only the phenomenal world standing. This leaves it standing, not even on the grave of the intelligible thing-in-itself, but on the grave of the living phenomenal itself. Concerning the old theological debate mentioned, if natural theology, even in the wide sense of Kant's moral reason indeed fails, it should give lutherans some philosophical leverage over natural religions.
